Left quotients of a C*-algebra, III: Operators on left quotients

Lawrence G. Brown; Ngai-Ching Wong

Studia Mathematica, Tome 215 (2013), p. 189-217 / Harvested from The Polish Digital Mathematics Library

Résumé

Let L be a norm closed left ideal of a C*-algebra A. Then the left quotient A/L is a left A-module. In this paper, we shall implement Tomita’s idea about representing elements of A as left multiplications: $π_{p} (a) (b + L) = a b + L$ . A complete characterization of bounded endomorphisms of the A-module A/L is given. The double commutant $π_{p} {(A)}^{''}$ of $π_{p} (A)$ in B(A/L) is described. Density theorems of von Neumann and Kaplansky type are obtained. Finally, a comprehensive study of relative multipliers of A is carried out.

Publié le : 2013-01-01

Zbl 1294.46046

EUDML-ID : urn:eudml:doc:285821

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-3-1,
     author = {Lawrence G. Brown and Ngai-Ching Wong},
     title = {Left quotients of a C*-algebra, III: Operators on left quotients},
     journal = {Studia Mathematica},
     volume = {215},
     year = {2013},
     pages = {189-217},
     zbl = {1294.46046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-3-1}
}

Lawrence G. Brown; Ngai-Ching Wong. Left quotients of a C*-algebra, III: Operators on left quotients. Studia Mathematica, Tome 215 (2013) pp. 189-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-3-1/